Simplify the following expression: $ q = \dfrac{t + 5}{4} - \dfrac{-8}{3} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{3}{3}$ $ \dfrac{t + 5}{4} \times \dfrac{3}{3} = \dfrac{3t + 15}{12} $ Multiply the second expression by $\dfrac{4}{4}$ $ \dfrac{-8}{3} \times \dfrac{4}{4} = \dfrac{-32}{12} $ Therefore $ q = \dfrac{3t + 15}{12} - \dfrac{-32}{12} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{3t + 15 + 32 }{12} $ Distribute the negative sign: $q = \dfrac{3t + 15 + 32}{12}$ $q = \dfrac{3t + 47}{12}$